Variance of the Isotropic Uniform Systematic Sampling

Authors

  • Jiri Janacek Institute of Physiology, ASCR, v.v.i.
  • Daniel Jirak Institute for Clinical and Experimental Medicine First Faculty of Medicine

DOI:

https://doi.org/10.5566/ias.2218

Keywords:

isotropic design, spatial statistics, stereology, systematic sampling, variance

Abstract

The integral of a smooth function with bounded support over a set with finite perimeter in Euclidean space ℝd is estimated using a periodic grid in an isotropic uniform random position. Extension term in the estimator variance is proportional to the integral of the squared modulus of the function over the object boundary and to the grid scaling factor raised to the power of d+1. Our result generalizes the Kendall-Hlawka-Matheron formula for the variance of the isotropic uniform systematic estimator of volume.

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Published

2019-12-13

Issue

Section

Original Research Paper

How to Cite

Janacek, J., & Jirak, D. (2019). Variance of the Isotropic Uniform Systematic Sampling. Image Analysis and Stereology, 38(3), 261-267. https://doi.org/10.5566/ias.2218

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